Difficulty: Easy

Average Score: 75%

The regression equation y = 980 + 310x (x = team size, y = budget amount) What is the appropriate interpretation of this equation?

Rationale

An increase of 1 in the team size is associated with an increase in the budget of $310.

In the regression equation y = 980 + 310x, the coefficient of x (team size) indicates that for every additional team member, the budget (y) increases by $310. This illustrates the relationship between team size and budget allocation.

A (An increase of 310 in the team size is associated with an increase in the budget of $1.) YOUR ANSWER

This interpretation incorrectly suggests that a substantial increase in team size (310) would yield a minimal budget increase of just $1, which misrepresents the coefficient in the regression equation. The equation indicates that the budget increases by $310 for each individual increase in team size, not for a change of 310.

B (An increase of 980 in the team size is associated with an increase in the budget of $1.) YOUR ANSWER

This option misinterprets the constant term (980) in the regression equation. The number 980 represents the baseline budget when the team size is zero, not a change in team size. Therefore, it does not appropriately relate team size changes to budget increases.

C (An increase of 1 in the team size is associated with an increase in the budget of $980.) YOUR ANSWER

This choice also misrepresents the regression coefficient. While it correctly identifies the change related to an increase in team size, it incorrectly states that the budget increases by $980 rather than the correct amount of $310.

Conclusion

The regression equation clearly indicates that an increase of 1 in team size corresponds to a $310 increase in the budget. Understanding the coefficients in a regression equation is crucial for interpreting the relationship between variables accurately. Misinterpretations can lead to substantial errors in decision-making based on the data.

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